Context. There is still a debate about the nature of the mechanism that causes the pulsation excitation of the rapidly oscillating Ap stars that oscillate above the highest theoretically acoustic frequency. HD 24712 is a good test case for such a study because it is bright, its parallax accurately determined, and its frequency spectrum is well known. Aims. Visible long-baseline interferometry is a unique technique for measuring accurate angular diameters of targets as small as the brightest roAp stars, and thus estimating accurate radii by a method as independent as possible of atmosphere models. Methods. We used the visible spectrograph VEGA at the CHARA long-baseline optical array to observe HD 24712, and we derived its limb-darkened diameter. We also estimated its bolometric flux from spectroscopic data in the literature and determined its radius, luminosity, and effective temperature. Results. We determined a limb-darkened angular diameter of 0.335 ± 0.009 mas for HD 24712 and derived a radius of R = 1.772 ± 0.057 R⊙, a luminosity of L = 7.2 ± 1.8 L⊙, and an effective temperature of Teff = 7235 ± 280 K, which is in very close agreement with the values provided by the self-consistent stratified model developed for this star. We used these fundamental parameters to set HD 24712 in the Hertzsprung-Russell diagram. Its position is marginally consistent with the region where high radial order modes are predicted to be excited by the κ-mechanism. Conclusions. We conclude that oscillations in this star are most likely not driven by the κ-mechanism.